Alice Bache Gould: mathematician in search of war work, 1918

Alliances between American mathematics and the military were not well defined when the United States entered World War I in April of 1917. Although academic mathematicians – like other American faculty members and students – were among the strongest supporters of the cause, it took time to identify how and where to utilize their technical training in the war effort. This paper investigates the case of Alice Bach Gould, one of E H Moore's mathematics graduate students at the University of Chicago, and her efforts to support US military endeavors with her scientific expertise. Although Gould's substantial research accomplishments in Spanish archives eventually surpassed her mathematical achievements, her quest for war work in 1917 nonetheless illustrates the difficulty of contributing mathematical training to patriotic service in the United States during World War I.     

Lessons From the Past Look to the Future

Dr. Howden is now formally retired from a long career teaching mathematics in elementary school through graduate level, editing and coauthoring mathematics textbooks, serving as District Mathematics Coordinator K‐12 for the Albuquerque, New Mexico, Public Schools, writing numerous professional articles, and participating on the writing team of the Curriculum and Evaluation Standards for School Mathematics. She now enjoys long walks with her dog Quincy, “becoming increasingly aware, of mathematics all around us: patterns of leaf growth, distances between consecutive veins in leaves, kinds of ant hills, snake trails in the sand, bird call patterns.” She plans to relate many such examples to mathematical patterns in the book she is currently writing.     

“Mathematicians Would Say It This Way”: An Investigation of Teachers' Framings of Mathematicians

Although popular media often provides negative images of mathematicians, we contend that mathematics classroom practices can also contribute to students' images of mathematicians. In this study, we examined eight mathematics teachers' framings of mathematicians in their classrooms. Here, we analyze classroom observations to explore some of the characteristics of the teachers' framings of mathematicians in their classrooms. The findings suggest that there may be a relationship between a teachers' mathematics background and his/her references to mathematicians. We also argue that teachers need to be reflective about how they represent mathematicians to their students, and that preservice teachers should explore their beliefs about what mathematicians actually do.     

Images of mathematicians: a new perspective on the shortage of women in mathematical careers

Though women earn nearly half of the mathematics baccalaureate degrees in the United States, they make up a much smaller percentage of those pursuing advanced degrees in mathematics and those entering mathematics-related careers. Through semi-structured interviews, this study took a qualitative look at the beliefs held by five undergraduate women mathematics students about themselves and about mathematicians. The findings of this study suggest that these women held stereotypical beliefs about mathematicians, describing them to be exceptionally intelligent, obsessed with mathematics, and socially inept. Furthermore, each of these women held the firm belief that they do not exhibit at least one of these traits, the first one being unattainable and the latter two being undesirable. The results of this study suggest that although many women are earning undergraduate degrees in mathematics, their beliefs about mathematicians may be preventing them from identifying as one and choosing to pursue mathematical careers.     

Confluences of agendas: Emigrant mathematicians in transit in Denmark, 1933–1945

The present paper analyses the confluence of agendas held by Danish mathematicians and German refugees from Nazi oppression as they unfolded and shaped the mathematical milieu in Copenhagen during the 1930s. It does so by outlining the initiatives to aid emigrant intellectuals in Denmark and contextualises the few mathematicians who would be aided. For most of those, Denmark would be only a transit on the route to more permanent immigration, mainly in the US. Thus, their time in Copenhagen would exert only temporary influence over Danish mathematics; but as it will be argued, the impacts of their transit would be more durable both for the emigrants and for the Danish mathematical milieu. It is thus argued that the influx of emigrant mathematicians helped develop the institutional conditions of mathematics in Copenhagen in important ways that simultaneously bolstered the international outlook of Danish mathematicians. These confluences of agendas became particularly important for Danish mathematics after the war, when the networks developed during the 1930s could be drawn upon.     

Methodological conceptualization of mathematical modelling

The experience of the author and colleges, as mathematicians working in interdisciplinary groups, have shown the necessity to make the process of mathematical modelling more precise and to establish its different phases. In this way, the specific role of the mathematician in working teams can be better understood by the other members of the team and his or her specific capabilities can be used more efficiently. The proposed structuration of the mathematical modelling process is resumed in a following diagram, especially when computational schemes are the desired result (see Figure 1).

The discussion tends to delineate a concept of modelling from a standpoint where the difference between mathematics as a language and mathematics as a science, having its own dynamic and semantics, plays a fundamental role.     

‘There are great alterations in the geometry of late’. The rise of Isaac Newton’s early Scottish circle†

This paper traces the rise of three Scottish mathematicians – Colin Campbell, John Craig, and David Gregory – to become key figures in the dissemination and promotion of Newton’s mathematical ideas and natural philosophy in the 1680s. Two medical men – Archibald Pitcairne and his former student George Cheyne – both likewise captivated by the Principia, played minor roles in the story of Newton’s mathematics, while at the same time promoting the concept of mathematical medicine derived from his philosophical thought. Drawing on contemporary correspondence and previously unpublished papers, it considers how these men contributed to the scholarly perception of Newton and how, conversely, Newton used his increasing influence in order to encourage their work, most notably obtaining for Gregory the vacant chair in astronomy at Oxford in 1691.     

Researching how professional mathematicians construct new mathematical definitions: a case study

In this work, we study the mathematical practice of defining by mathematics researchers. Since research is an important part of many professional mathematicians, understanding how they do research is a necessary step before thinking about future researchers’ undergraduate and postgraduate education. We focus on the defining process associated with the generalization of existing definitions as a way of constructing new ones. Data of this qualitative study come from a case study whose subject is a mathematics researcher in the area of differential geometry. We have interviewed this researcher and collected her research documents. From our analysis of the data, we have identified four phases in the defining process (Finding an opportunity to generalize an existing concept, Proposing a new definition, Justifying that the new definition is valid and Continuing the chain of definitions), which we will describe in detail in Section 4.     

The visibility of models: using technology as a bridge between mathematics and engineering

Engineering mathematics is traditionally conceived as a set of unambiguous mathematical tools applied to solving engineering problems, and it would seem that modern mathematical software is making the toolbox metaphor ever more appropriate. The validity of this metaphor is questioned and the case is made that engineers do in fact use mathematics as more than a set of passive tools— that mathematical models for phenomena depend critically on the settings in which they are used and the tools with which they are expressed. The perennial debate over whether mathematics should be taught by mathematicians or by engineers looks increasingly anachronistic in the light of technological change, and the authors suggest that it is more instructive to examine the potential of technology for changing the relationships between mathematicians and engineers, and for connecting their respective knowledge domains in new ways.     

Theodore Strong and ante-bellum American mathematics

Theodore Strong was a prolific contributor to the mathematical and scientific journals of ante-bellum America. His work was not remarkable in its originality, but it dealt with mathematics that was quite sophisticated for its time and place. Strong's published work was a significant factor in the dissemination of advanced mathematics to his countrymen, and he played an important role in the education of a few mathematicians who were active in the latter part of the 19th century, most notably George William Hill.     

Breaking social barriers: Florentia Fountoukli (1869–1915)

During the nineteenth century the foundations were laid for the advance of female education. At the same time it was still not easy for women to enter the fields of mathematics and science. In Greece the situation was worse than in some other countries: women were not allowed to matriculate at Athens University until the last decades of the century. Florentia Fountoukli was the first Greek woman to attend lectures at the mathematics department. Her dream of becoming a mathematician was partly fulfilled after a long struggle to persuade university professors to accept her in their lectures as a regular student. Florentia was a talented person who in the end had little choice but to teach philosophy and pedagogy in an Arsakeion school. This paper sheds light on her professional life in the school in Corfu. Finally after four years of service she went to Athens where she set up and managed her own school.

(For another article on the mathematical education of women in the nineteenth century see Marit Hartveit's ‘How Flora got her cap’ in BSHM Bulletin, 24 (2009), 147–158.)     

Teacher listening: The role of knowledge of content and students

In this research report we consider the kinds of knowledge needed by a mathematician as she implemented an inquiry-oriented abstract algebra curriculum. Specifically, we will explore instances in which the teacher was unable to make sense of students’ mathematical struggles in the moment. After describing each episode we will examine the instructor's efforts to listen to the students and the way that these efforts were supported or constrained by her mathematical knowledge for teaching. In particular, we will argue that in each case the instructor was ultimately constrained by her knowledge of how students were thinking about the mathematics.     

Princess Elizabeth of Bohemia and Descartes’ letters (1650–1665)

After Descartes’ death in 1650, Princess Elizabeth generously shared with others several letters she had received from the philosopher, which contained philosophically as well as mathematically exciting material. In this article I place the transmission of these copies in context, revealing that Elizabeth steadily became an intellectually inspiring figure, attracting international attention. In the 1650s she stayed at Heidelberg where she discussed Cartesian philosophy with professors and students alike, including the professor of philosophy and mathematics Johann von Leuneschlos. In the mid-1660s, an initiative was taken from the English side of the Channel (Pell, More) to obtain Descartes’ mathematical letters to Elizabeth that had not yet been published. One letter of Elizabeth herself on this very subject has been preserved. The letter, addressed to Theodore Haak, will be published here for the first time. It is of special interest, because the princess supplies a general outline of her solution to the mathematical problem Descartes gave her to solve in 1643. It substantiates the hypothesis regarding Elizabeth’s solution earlier proposed by Henk Bos.     

An Experiment in Teaching College Mathematics†

Kac has observed that the ideal preparation in mathematics, especially for non‐mathematicians, should focus not on acquiring skills but on acquiring certain attitudes. We administered a special attitude questionnaire to a sample of graduate students in mathematics and undergraduate speech majors. We found significant differences on 10 of 27 items on this test. We then administered this test to a mixed group of undergraduates at the beginning and at the end of a special experimental mathematics ‘course’ designed to modify and shape attitudes. We found changes in attitudes in the intended direction. The primary aims of the experimental course were to:

1. Get students without any prior acquaintance with mathematics or a fear thereof to approach their studies more analytically.

2. Acquire orientation to and acquaintance with 25‐75 basic concepts and methods covering sets, algebra, logic, computers, analysis, probability, math‐statistics and topology in an over‐all map of how they logically fit together and how they relate to problems of modern life.

3. Read, with appreciation, mathematical literature previously incomprehensible to them. These aims were met.

     

Nominalism and constructivism in seventeenth-century mathematical philosophy

This paper argues that the philosophical tradition of nominalism, as evident in the works of Pierre Gassendi, Thomas Hobbes, Isaac Barrow, and Isaac Newton, played an important role in the history of mathematics during the 17th century. I will argue that nominalist philosophy of mathematics offers new clarification of the development of a “constructivist” tradition in mathematical philosophy. This nominalist and constructivist tradition offered a way for contemporary mathematicians to discuss mathematical objects and magnitudes that did not assume these entities were real in a Platonic sense, and helped lay the groundwork for formalist and instrumentalist approaches in modern mathematics.